With G Suite Sync for Microsoft® Outlook® (GSSMO), you can use Outlook to send messages from any email address you own—not just your primary G Suite address. This can be an email alias associated with your G Suite account, or an address from another account you own, such as your personal home address.

You add a custom From address in your Gmail Settings. After that, you can enter the address in the From field of messages you send from Outlook, and recipients will see that address listed as sender. Their replies will go to that address, too. You can also make a custom address your default From address, which is what recipient's see if you leave the From field blank.

  1. In Gmail, go to your Settings > Account tab.
  2. Add and verify your custom From address using the Send mail as settings. Do this as described at Adding a custom From address.
     A custom From address must be a working address where you can receive mail. This can be an external address for another account, or an alias for your G Suite account. (Aliases are created by your domain administrator as described at Add an email alias.)
  3. Optionally make the address your default From address by clicking its make default link in your Gmail Settings. After that, if you leave the From field blank in Outlook, recipients will see this default address as the sender, rather than your primary G Suite address.
  4. In Outlook, open a send window to choose from a list of available addresses. If you're using Microsoft Outlook 2010 or earlier, you might need to enter the whole address in the message's From field the first time. After that, the address autocompletes when you type the first few characters.
    Send from other email address

    Remember that the address has to be a verified address added in Gmail for the message to successfully be sent.
  5. Compose the rest of your message in Outlook and click Send.

Replying as a custom sender: You might receive messages sent to one of your custom addresses, as well (if the address is an email alias for your G Suite account, for example). When you reply, GSSMO assumes you want to reply as the same sender and therefore re-enters the address in the From field for you.

reply as a custom sender

Source: https://support.google.com/a/users/answer/190936?hl=en&ref_topic=29321